{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "import numpy as np\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1,  1,  0],\n",
       "       [-1,  0,  1],\n",
       "       [ 0, -1,  1]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[-1, 1, 0], [-1,0,1], [0, -1, 1]], np.int64)\n",
    "a\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left\\{ 0 : 1, \\  - i : 1, \\  i : 1\\right\\}$"
      ],
      "text/plain": [
       "{0: 1, -ⅈ: 1, ⅈ: 1}"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Matrix(a).eigenvals()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[ \\left( 0, \\  1, \\  \\left[ \\left[\\begin{matrix}1\\\\1\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( - i, \\  1, \\  \\left[ \\left[\\begin{matrix}- \\frac{\\left(-1 - i\\right) \\left(1 - i\\right)}{2 \\left(1 + i \\left(-1 + i\\right)\\right)}\\\\- \\frac{-1 + i}{1 + i \\left(-1 + i\\right)}\\\\1\\end{matrix}\\right]\\right]\\right), \\  \\left( i, \\  1, \\  \\left[ \\left[\\begin{matrix}- \\frac{\\left(-1 + i\\right) \\left(1 + i\\right)}{2 \\left(1 - i \\left(-1 - i\\right)\\right)}\\\\- \\frac{-1 - i}{1 - i \\left(-1 - i\\right)}\\\\1\\end{matrix}\\right]\\right]\\right)\\right]$"
      ],
      "text/plain": [
       "⎡               ⎛       ⎡⎡-(-1 - ⅈ)⋅(1 - ⅈ) ⎤⎤⎞  ⎛      ⎡⎡-(-1 + ⅈ)⋅(1 + ⅈ) ⎤⎤\n",
       "⎢               ⎜       ⎢⎢──────────────────⎥⎥⎟  ⎜      ⎢⎢──────────────────⎥⎥\n",
       "⎢⎛      ⎡⎡1⎤⎤⎞  ⎜       ⎢⎢2⋅(1 + ⅈ⋅(-1 + ⅈ))⎥⎥⎟  ⎜      ⎢⎢2⋅(1 - ⅈ⋅(-1 - ⅈ))⎥⎥\n",
       "⎢⎜      ⎢⎢ ⎥⎥⎟  ⎜       ⎢⎢                  ⎥⎥⎟  ⎜      ⎢⎢                  ⎥⎥\n",
       "⎢⎜0, 1, ⎢⎢1⎥⎥⎟, ⎜-ⅈ, 1, ⎢⎢    -(-1 + ⅈ)     ⎥⎥⎟, ⎜ⅈ, 1, ⎢⎢    -(-1 - ⅈ)     ⎥⎥\n",
       "⎢⎜      ⎢⎢ ⎥⎥⎟  ⎜       ⎢⎢  ──────────────  ⎥⎥⎟  ⎜      ⎢⎢  ──────────────  ⎥⎥\n",
       "⎢⎝      ⎣⎣1⎦⎦⎠  ⎜       ⎢⎢  1 + ⅈ⋅(-1 + ⅈ)  ⎥⎥⎟  ⎜      ⎢⎢  1 - ⅈ⋅(-1 - ⅈ)  ⎥⎥\n",
       "⎢               ⎜       ⎢⎢                  ⎥⎥⎟  ⎜      ⎢⎢                  ⎥⎥\n",
       "⎣               ⎝       ⎣⎣        1         ⎦⎦⎠  ⎝      ⎣⎣        1         ⎦⎦\n",
       "\n",
       "⎞⎤\n",
       "⎟⎥\n",
       "⎟⎥\n",
       "⎟⎥\n",
       "⎟⎥\n",
       "⎟⎥\n",
       "⎟⎥\n",
       "⎟⎥\n",
       "⎠⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1 = Matrix(a).eigenvects()\n",
    "a1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}i\\\\1 + i\\\\1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡  ⅈ  ⎤\n",
       "⎢     ⎥\n",
       "⎢1 + ⅈ⎥\n",
       "⎢     ⎥\n",
       "⎣  1  ⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(a1[1][2][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}- i\\\\1 - i\\\\1\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡ -ⅈ  ⎤\n",
       "⎢     ⎥\n",
       "⎢1 - ⅈ⎥\n",
       "⎢     ⎥\n",
       "⎣  1  ⎦"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(a1[2][2][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
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  "language_info": {
   "codemirror_mode": {
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